EL DESARROLLO Y LA EVOLUCIÓN DE LA CALIDAD EN LOS SERVICIOS DEL

Both in acknowledgement of the novelty of this modelling approach and the extreme uncertainty in reaction rates at very high tem peratures and densities (as well as with highly electronically and ro-vibrationally excited species) we select an extremely simple chem istry between ju st twenty four species as listed in table 5.1. The selection criteria are similar to those used for the early chemistry: small molecules are chosen to model the m ajor component of the chemistry, leaving out the larger molecules which are likely to have low abundances, increasing the likelihood of numerical stiffness in the ODEs. A simple oxygen chemistry is included so as to model the formation and longevity of CO in a hydrodynamically complex flow.

A hydrocarbon chemistry has a simplicity th a t makes analysis of these very early results easier; a complex chemistry would make it more difficult to evaluate the model as a whole. One could argue th a t the most appropriate course of action would be to use

156 CHAPTER 5. A FLUID DYNAMIC MODEL

H C 0 H+ C+ 0 +

H -

c-

OH CH CO H+

c+

CH+ 0H + C 0 + HCO HCO+

Table 5.1: Species selected for CFD modelling.

the entire early-tim e chemistry as developed in chapter 3 in order th a t direct comparison

be possible. W hilst good in principle, these rates are unsuited to environments having very high tem peratures and densities thus leading to uncertainties already mentioned. Furtherm ore, such a large chemistry is simply impractical given the considerable run time of these models on readily available computers: using DEC Alpha workstations, often sharing with other users, a model running even on the fastest (500 Mhz) processors may take many days or weeks to complete. It has already been found in the chemical models of previous chapters th a t the more complex a chemistry becomes, the greater the chance of numerical stiffness developing. The CFD code appears (from experience) to be less able to deal with stiffness than the chemical codes equipped with integration algorithm s tuned for stiff equations, and is easily forced to use very small time-steps where <C 1 sec;

many models, including some presented in this chapter, recorded an average time-step of ~ 0.2seconds. Small time-steps result in many more steps being required to model a

given period of evolution and a proportional increase in the number of cycles required to com pute the chemical terms; the larger the chemistry, the greater the probability of small tim e-steps being required. It should also be considered th a t neither a chemical kinetic nor hydrodynamic model offers a complete solution for the study of dynamic outflows: using the two together is likely to prove quite powerful. For example, chemical kinetic models may be used to analyse in detail regions of interest identified within dynamic models executed both with and w ithout chemistry. In this way the detailed chemistry of ju st one region of interest may be modelled with a very specific reaction network which might be quite inappropriate to other regions in a CFD model grid.

T he reaction network is limited to ju st 224 reactions extracted from the early tim e rate file used in the work of chapter 3. All rate coefficients are calculated correctly for those reactions with rates not com puted from the Arrhenius equation including the collisional dissociation of CO and three-body reactions (as described in chapter 3). Nitrogen is

5.4. LIMITATIONS 157

notably absent from this species set and rate file. Although im portant, the complete addition of im portant species involving this element, with all reaction networks from the early chemistry involving nitrogen bearing species, and those species chosen for CFD modelling would result in the rate-file having an ex tra 352 reactions thus more than doubling the size of the chemistry. It was felt th a t, although a reduced nitrogen network could be introduced a t this time, making a working model was sufficiently problem atic th a t simplicity seemed to be the key to early success. Once confidence has been gained with CFD modelling, a complete nitrogen chemistry will be introduced.

5.4

L im itations

Hydrodynamic codes require considerable processor time as a result of their calculating the physical param eters a t each grid point many millions of times. For greater resolution more grid points are required and execution time increases in direct proportion. The addition of chemistry also adds to the com putational load as each chemical species is treated as a separate fluid element. If the environment being modelled is relatively homogeneous, the chemistry will be approxim ately in equilibrium throughout the grid and, providing there are no discontinuities in physics, the chemical time-step at each grid point will be large. Provided th a t this tim e-step is smaller than th a t of the dynamics, the la tte r will govern the overall speed of execution. However, in modelling nova outflows we introduce huge discontinuities in both the tem perature and density across the grid. The prime example is th a t of the interface between the expanding shell and the interstellar medium into which it is forced. Across this boundary the density may jum p seven or more orders of m agnitude whilst the gas tem perature jum ps from a few hundred or thousands to several million Kelvin. This is as a result of the strong non-adiabatic shock th a t develops where the high velocity and high density shell meets the static, low density ISM m aterial. W hilst in such extremely hot regions the chemistry is ‘turned off’ because the gas will be a plasm a and the gas-phase chemistry of no relevance, there may be other regions where the chemical tim e-step becomes very small and dominates, forcing the model to creep along with tiny steps, slowly working across difficult zones.

The ionisation of the medium within this model is due entirely to the reaction net­ works involved; unlike the chemical kinetics models, no inclusion of electrons from low ionisation potential metals is made nor are any other assumptions about th e ionisation of

158 CHAPTER 5. A FLUID DYN AMIC MODEL

the m aterial. This is the best th a t can be done currently.

5 .4 .1 P h o t o c h e m is t r y

In contrast to the chemical kinetics models th a t boast a new and sophisticated treatm ent of photorates with realistic radiation fields, this model takes an extremely basic approach. The CFD code was originally w ritten specifically to model astrophysical jets, colliding winds, molecular clouds in which some dynamic activity is occurring and other regions th a t differ from the nova most crucially in term s of the im portance of photoreactions and the nature of the radiation field. T h at said, shock regions do generate strong UV fields but this can be assumed to be approximately uniform throughout a shock region which makes it relatively easy to incorporate photoreactions. W ith the code as it stands, incorporating an intense, directional radiation field appropriate to the nova environm ent is not practical w ithout considerable modification. This task will be approached once it has been confirmed th a t a CFD solution to the nova problem is valid and effective, as shall be achieved in this work. Until such time, the radiation field is fixed at all points and times throughout the model.